In [1]}, Bravo, Herrera and Ramírez presented some combinatorial interpretations for these \(k\) -Pell numbers while in [2]}, Bravo, Herrera and Luca determined a Binet-style formula for these sequences and proved several results on the asymptotic behavior of the dominant root of their characteristic equation. Furthermore, as shown in [2]}, the sequences of order-\(k\)  Pell numbers have a good asymptotic behavior, as well as the sequences of \(k\) -generalized Fibonacci numbers.
